Optimal Stiffness Parameters of the Turbine Bladed Disk Computational Model

2013 ◽  
Author(s):  
Pavel Polach
Keyword(s):  
Computational Model ◽  
Steam Turbine ◽  
Topical Application ◽  
Natural Vibration ◽  
Natural Frequencies ◽  
Mode Shapes ◽  
Centrifugal Forces ◽  
Bladed Disk ◽  
Real Contact ◽  
Optimal Stiffness

Motivation for introducing this paper is the topical application of the method using the rotational periodicity of the structure at calculating natural vibration characteristics of the steam turbine bladed disk with continuous binding, in this case in the form of integral shrouding and in the middle of the blade with the tie-boss connection. Part of the shroud and the part of the tie-boss are the integral parts of the blade. Blades are free at non-rotating bladed disk. Blades of the advanced design are continuously coupled in the zone of the shroud and in the tie-boss zone by the blades untwist caused by the centrifugal forces acting at turbine rotation. The method used for the calculation of natural frequencies and mode shapes of the bladed disk with the continuous binding does not enable to model the real contact properties. The contact must be modeled by the flexible connection. The stiffness of the connection in the zones of adjoining blades contact is “tuned” at turbine operational speed (i.e. at 3000 rpm) in such a way that the values of calculated natural frequencies may come as near as possible to the values of the measured natural frequencies.

Finding the Stiffnesses of Interface Contact Elements for the Computational Model of Steam Turbine Blading

2017 ◽  
Author(s):  
Josef Voldřich ◽  
Jan Lazar ◽  
Pavel Polach ◽  
Štefan Morávka
Keyword(s):  
Computational Model ◽  
Steam Turbine ◽  
Nonlinear Dynamic ◽  
Natural Frequencies ◽  
Resonant Response ◽  
Nonlinear Dynamic Model ◽  
Interface Elements ◽  
Bladed Disk ◽  
Interface Contact ◽  
Turbine Blading

A method is proposed for fitting the so-called contact stiffnesses (CSs) of interface elements for a nonlinear dynamic model (NDM) of a bladed disk with integral contact couplings. The method is based on comparison between frequencies of the resonant response of NDM and known natural frequencies in limiting linear cases. For this purpose, an effective approach for calculation of the resonant response NDM is presented allowing CSs to be picked individually. The method is demonstrated for the case of steam turbine bladed disk equipped with 48 inch blades.

Free Vibration in a Mistuned Steam Turbine Last Stage Bladed Disk

2015 ◽  
Author(s):  
Marcin Drewczynski ◽  
Romuald Rzadkowski ◽  
Artur Maurin ◽  
Piotr Marszalek
Keyword(s):  
Steam Turbine ◽  
Natural Frequencies ◽  
Numerical Study ◽  
Mode Shapes ◽  
Fem Model ◽  
Bladed Disk ◽  
Turbine Efficiency ◽  
Pressure Steam ◽  
Fourth Series ◽  
Last Stage

The design of blades in the last stage of a steam turbine is one of the most demanding engineering tasks in the turbomachinery field. Increasing turbine efficiency has led to the designing of higher tip-to-hub ratios. Slender blading conforms to reliability requirements, such as high blade stiffness and a high first mode natural frequency. Several high vibration amplitude problems were reported regarding a slender last stage blading of a commercial low-pressure steam turbine. During maintenance it was decided that the blades would be geometrically mistuned to prevent self-excitation. This paper presents a numerical study of LP steam turbine last stage bladed disk mistuning. Two different approaches to mistuning were applied and numerically compared: geometrical and material. The mode shapes and natural frequencies of the steam turbine bladed disk were calculated on the basis of an FEM model. The smallest range of mistuning (0,5Hz) in a bladed disk contaminates nodal diameters up to the fourth series. This should be taken into account when tip-timing method is adapted for steam turbine operation monitoring.

scholarly journals High-Fidelity Sensitivity Analysis of Modal Properties of Mistuned Bladed Disks Regarding Material Anisotropy

2018 ◽  
Author(s):  
Adam Koscso ◽  
Guido Dhondt ◽  
E. P. Petrov
Keyword(s):  
Sensitivity Analysis ◽  
Finite Element ◽  
Natural Frequencies ◽  
Mode Shapes ◽  
Finite Element Models ◽  
Coordinate Systems ◽  
Bladed Disks ◽  
Bladed Disk ◽  
Material Orientation

A new method has been developed for sensitivity calculations of modal characteristics of bladed disks made of anisotropic materials. The method allows the determination of the sensitivity of the natural frequencies and mode shapes of mistuned bladed disks with respect to anisotropy angles that define the crystal orientation of the monocrystalline blades using full-scale finite element models. An enhanced method is proposed to provide high accuracy for the sensitivity analysis of mode shapes. An approach has also been developed for transforming the modal sensitivities to coordinate systems used in industry for description of the blade anisotropy orientations. The capabilities of the developed methods are demonstrated on examples of a single blade and a mistuned realistic bladed disk finite element models. The modal sensitivity of mistuned bladed disks to anisotropic material orientation is thoroughly studied.

Forced Vibration of Mistuned Bladed Discs in Last Stage LP Steam Turbine

2016 ◽  
Author(s):  
Romuald Rzadkowski ◽  
Artur Maurin ◽  
Leszek Kubitz ◽  
Ryszard Szczepanik
Keyword(s):  
Steam Turbine ◽  
Forced Vibration ◽  
Natural Frequencies ◽  
Mode Shapes ◽  
Lower Stress ◽  
Free And Forced Vibrations ◽  
Specific Order ◽  
Last Stage ◽  
Forced Vibration Analysis ◽  
Blade Geometry

During the exploitation of a commercial LP steam turbine, self-excitation occurred in the last stage of slender blades, inducing high vibration amplitudes. These problems were solved by changing the geometry of certain blades (feathering) and arranging them in a specific order (alternating mistuning). This paper presents free and forced vibrations of various mistuned steam turbine bladed discs. The natural frequencies and mode shapes of the steam turbine bladed discs were calculated using FEM models. Two different approaches to mistuning were applied: either the blade geometry or the Young’s Modulus were changed. Next, the results were compared. This showed that blade geometry mistuning gave the best results for long blades in the case of higher mistuning. The forced vibration analysis showed that the maximal blade stress location differed, depending on the kind of mistuning. The application feathering and alternating mistuning showed lower stress levels than the tip-timing measured standard mistuning pattern.

Study on the Natural Vibration Characteristics of Flexible Missile With Thrust by Using Riccati Transfer Matrix Method

2015 ◽  
Vol 83 (3) ◽  
Author(s):  
Gangli Chen ◽  
Xiaoting Rui ◽  
Fufeng Yang ◽  
Jianshu Zhang
Keyword(s):  
Transfer Matrix ◽  
Transfer Matrix Method ◽  
Matrix Method ◽  
Natural Vibration ◽  
Natural Frequencies ◽  
Compressive Force ◽  
Vibration Characteristics ◽  
Mode Shapes ◽  
Engine Thrust ◽  
Natural Vibration Characteristics

Due to the mass consumption and engine thrust of a flexible missile during the powered phase flight, its natural vibration characteristics may be changed significantly. The calculation of natural frequencies and mode shapes plays an important role in the structural design of the missile. Aiming at calculating the natural vibration characteristics of the missile rapidly and accurately, a nonuniform beam subjected to an engine thrust is used to model the free vibration of the missile and Riccati transfer matrix method (RTMM) is adopted in this paper. Numerical results show that the natural frequencies of a typical single stage flexible missile are increased unceasingly in its powered phase, and its mode shapes are changed a lot. When the presented methodology is used to study the natural vibration characteristics of flexible missiles, not only the mass, stiffness, and axial compressive force distributions are described realistically but also numerical stability, high computation speed, and accuracy are achieved.

A Perturbation Solution of the Thickness Natural Vibrations of a Piezoelectric Plate

2013 ◽  
Vol 136 (1) ◽  
Author(s):  
Piotr Cupiał
Keyword(s):  
Boundary Conditions ◽  
Electrostatic Potential ◽  
Natural Vibration ◽  
Natural Frequencies ◽  
Piezoelectric Plate ◽  
Perturbation Solution ◽  
Mode Shapes ◽  
Perturbation Approach ◽  
Linear Piezoelectricity ◽  
Coupled Theory

This paper discusses a perturbation approach to the calculation of the natural frequencies and mode shapes for both the displacement and the electrostatic potential through-thickness vibration of an infinite piezoelectric plate. The problem is formulated within the coupled theory of linear piezoelectricity. It is described by a set of two coupled differential equations with unknown thickness displacement, the electrostatic potential and a general form of boundary conditions. A consistent perturbation solution to the natural vibration problem is described. An important element not present in the classical eigenvalue perturbation solution is that the small parameter appears in the boundary conditions; a way to handle this complication has been discussed. The natural frequencies and mode shapes obtained using the perturbation approach are compared to exact solutions, demonstrating the effectiveness of the proposed method. The advantage of the perturbation method derives from the fact that coupled piezoelectric results can be obtained from the elastic solution during the postprocessing stage.

Flutter and Forced Vibration Characteristics of a Turbo Fan Bladed Disk Rotor

2013 ◽  
Author(s):  
Madhavan Srinivasan ◽  
Sankarkumar Jeyaraman ◽  
Rajeev Jain ◽  
Sujatha Chandramohan ◽  
Sekhar AnandaRao Seshadri
Keyword(s):  
Forced Vibration ◽  
Natural Frequencies ◽  
Fluid Dynamic ◽  
Mode Shapes ◽  
Blade Vibration ◽  
Engine Operation ◽  
Bladed Disk ◽  
Blade Flutter ◽  
Loss Of Thrust

Aero-elastic excitation can result in excessive blade vibration, which can cause blades to fail in high cycle fatigue (HCF). A severe aero-elastic failure can result in a complete blade separation and loss of thrust and loss of a blade can mean the loss of an aircraft. The primary aeromechanical design concerns are blade flutter and forced vibration that need to be quantified at the early part of engine tests. This paper details the experimental investigation carried out on a transonic shroudless low aspect ratio fan bladed disk that experienced subsonic/transonic stall flutter and forced vibration excitation. Experiments are performed on a full scale engine using tip timing sensors flush mounted on the fan casing to characterize the vibratory responses during flutter and forced vibration conditions during engine operation. Numerical simulations are performed using computational fluid dynamic (CFD) analysis. Blade natural frequencies and mode shapes are obtained from finite element (FE) modal analysis. The experimental data captured from engine tests are used to validate the predicted results.

Multistage Coupling of Eight Mistuned Bladed Disk on a Solid Shaft: Part 1—Free Vibration Analysis

2012 ◽  
Author(s):  
Romuald Rzadkowski ◽  
Artur Maurin
Keyword(s):  
Finite Element ◽  
Free Vibration ◽  
Vibration Analysis ◽  
Natural Frequencies ◽  
Free Vibration Analysis ◽  
Free Vibrations ◽  
Rotor Blades ◽  
Mode Shapes ◽  
Bladed Disk ◽  
Centrifugal Stiffening

Considered here was the effect of multistage coupling on the dynamics of a rotor consisting of eight mistuned bladed discs on a solid shaft. Each bladed disc had a different number of rotor blades. Free vibrations were examined using finite element representations of rotating single blades, bladed discs, and the entire rotor. In this study the global rotating mode shapes of eight flexible mistuned bladed discs on shaft assemblies were calculated, taking into account rotational effects such as centrifugal stiffening. The thus obtained natural frequencies of the blade, shaft, bladed disc and entire shaft with discs were carefully examined to discover resonance conditions and coupling effects. This study found that mistuned systems cause far more intensive multistage coupling than tuned ones. The greater the mistuning, the more intense the multistage coupling.

scholarly journals High-Fidelity Sensitivity Analysis of Modal Properties of Mistuned Bladed Disks Regarding Material Anisotropy

2018 ◽  
Vol 141 (2) ◽  
Author(s):  
Adam Koscso ◽  
Guido Dhondt ◽  
E. P. Petrov
Keyword(s):  
Sensitivity Analysis ◽  
Finite Element ◽  
Natural Frequencies ◽  
Mode Shapes ◽  
Finite Element Models ◽  
Coordinate Systems ◽  
Bladed Disks ◽  
Bladed Disk ◽  
Material Orientation

A new method has been developed for sensitivity calculations of modal characteristics of bladed disks made of anisotropic materials. The method allows the determination of the sensitivity of the natural frequencies and mode shapes of mistuned bladed disks with respect to anisotropy angles that define the crystal orientation of the monocrystalline blades using full-scale finite element models. An enhanced method is proposed to provide high accuracy for the sensitivity analysis of mode shapes. An approach has also been developed for transforming the modal sensitivities to coordinate systems (CS) used in industry for description of the blade anisotropy orientations. The capabilities of the developed methods are demonstrated on examples of a single blade and a mistuned realistic bladed disk finite element models. The modal sensitivity of mistuned bladed disks to anisotropic material orientation is thoroughly studied.

Mistuning Analyses of a Bladed Disk: Pole-Zero and Modal Approaches

2008 ◽  
Author(s):  
Alok Sinha
Keyword(s):  
Natural Frequencies ◽  
Peak Amplitude ◽  
Mode Shapes ◽  
Bladed Disk ◽  
Amplitude Maximum ◽  
Excitation Frequencies ◽  
Amplitude Amplification

This paper examines the fundamental aspects of amplitude amplification due to mistuning in a bladed disk. Both pole-zero and modal approaches are used to understand the effects of changes in mode shapes and the natural frequencies on the minimum and maximum values of peak amplitudes among all blades over all excitation frequencies. The nature of variation of this peak amplitude is studied, and algorithms are discussed to determine the statistics of the peak amplitude, maximum and minimum values of the peak amplitude, and corresponding mistuning patterns.

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